Advertisements
Advertisements
Question
Explain the phenomena of surface tension on the basis of molecular theory.
Advertisements
Solution
Molecular theory of surface tension:
- Let PQRS = Surface film of liquid in a container containing liquid. PS is the free surface of the liquid and QR is the inner layer parallel to PS at distance equal to the range of molecular force.
- Now consider three molecules A, B, and C in a liquid in a vessel such that molecule A is well inside the liquid, molecule B within the surface film, and molecule C is on the surface of the liquid as shown in the figure.
- The sphere of influence of molecule A is entirely inside the liquid. As a result, molecule A is acted upon by equal cohesive forces in all directions. Thus, the net cohesive force acting on molecule A is zero.
- For molecule B, a large part of its sphere of influence is inside the liquid and a smaller part is outside the surface (in the air). The adhesive force acting on molecule B due to air molecules above it and within its sphere of influence is weak compared to the strong downward cohesive force acting on the molecule. As a result, molecule B gets attracted inside the liquid.
- For molecule C, half of the sphere of influence is in air and half is in liquid. As the density of air is much less than that of liquid, the number of air molecules within the sphere of influence of molecule C above the free surface of the liquid is much less than the numbers of liquid molecules within the sphere of influence that lies within the liquid. Thus, the adhesive force due to the air molecules acting on molecule C is weak compared to the cohesive force acting on the molecule. As a result, molecule C also gets attracted inside the liquid.
- Thus, all molecules in the surface film are acted upon by an unbalanced net cohesive force directed into the liquid. Therefore, the molecules in the surface film are pulled inside the liquid. This minimizes the total number of molecules in the surface film. As a result, the surface film remains under tension. The surface film of a liquid behaves like a stretched elastic membrane. This tension is known as surface tension and the force due to it acts tangential to the free surface of a liquid.
RELATED QUESTIONS
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0.072 N/m, atmospheric pressure = 1.013 x 105 N/m2 ]
Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube.
Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section.
In which of the following substances, surface tension increases with increase in temperature ?
- Copper
- Molten copper
- Iron
- Molten iron
Fill in the blanks using the word(s) from the list appended with each statement
Surface tension of liquids generally . . . with temperatures (increases / decreases)
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
A big drop of radius R is formed from 1000 droplets of water. The radius of a droplet will be _______
A) 10 R
B) R/10
C) R/100
D) R/1000
The contact angle between water and glass is 0°. When water is poured in a glass to the maximum of its capacity, the water surface is convex upward. The angle of contact in such a situation is more than 90°. Explain.
The force of surface tension acts tangentially to the surface whereas the force due to air pressure acts perpendicularly on the surface. How is then the force due to excess pressure inside a bubble balanced by the force due to the surface tension?
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution in S, the work done in the process is
If more air is pushed in a soap bubble, the pressure in it
The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is
Water rises in a vertical capillary tube up to a length of 10 cm. If the tube is inclined at 45°, the length of water risen in the tube will be
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
Viscosity is a property of
A liquid is contained in a vertical tube of semicircular cross section. The contact angle is zero. The force of surface tension on the curved part and on the flat part are in ratio
Consider a small surface area of 1 mm2 at the top of a mercury drop of radius 4.0 mm. Find the force exerted on this area (a) by the air above it (b) by the mercury below it and (c) by the mercury surface in contact with it. Atmospheric pressure = 1.0 × 105 Pa and surface tension of mercury = 0.465 N m−1. Neglect the effect of gravity. Assume all numbers to be exact.
A capillary tube of radius 0.50 mm is dipped vertically in a pot of water. Find the difference between the pressure of the water in the tube 5.0 cm below the surface and the atmospheric pressure. Surface tension of water = 0.075 N m−1.
A ferry boat has internal volume 1 m3 and weight 50 kg.(a) Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water.(b) If a leak develops in the bottom and water starts coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?
Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.
Why is the surface tension of paints and lubricating oils kept low?
A u-tube is made up of capillaries of bore 1 mm and 2 mm respectively. The tube is held vertically and partially filled with a liquid of surface tension 49 dyne/cm and zero angles of contact. Calculate the density of the liquid, if the difference in the levels of the meniscus is 1.25 cm. take g = 980 cm/s2
How does surface tension help a plant?
Define the surface tension of a liquid.
How is surface tension related to surface energy?
What are the factors affecting the surface tension of a liquid?
What is capillarity?
A capillary of diameter d mm is dipped in water such that the water rises to a height of 30 mm. If the radius of the capillary is made `(2/3)` of its previous value, then compute the height up to which water will rise in the new capillary?
A spherical soap bubble A of radius 2 cm is formed inside another bubble B of radius 4 cm. Show that the radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is lesser than the radius of both soap bubbles A and B.
Why coffee runs up into a sugar lump (a small cube of sugar) when one corner of the sugar lump is held in the liquid?
Water rises in a capillary tube of radius r upto a height h. The mass of water in a capillary is m. The mass of water that will rise in a capillary of radius `"r"/4` will be ______.
Two small drops of mercury each of radius 'R' coalesce to form a large single drop. The ratio of the total surface energies before and after the change is ____________.
If the surface tension of a soap solution is 3 × 10-2 N/m then the work done in forming a soap film of 20 cm × 5 cm will be ______.
A large number of liquid drops each of radius 'r' coalesce to form a big drop of radius 'R'. The energy released in the process in converted into kinetic energy of the big drop. The speed of the big drop is ______. (T = surface tension of liquid, p = density of liquid)
A molecule of water on the surface experiences a net ______.
A water drop of radius R' splits into 'n' smaller drops, each of radius 'r'. The work done in the process is ______.
T = surface tension of water
What is surface tension? Explain the applications of surface tension.
The length of a needle floating on water is 2 cm. The additional force due to surface tension required to pull the needle out of water will be (S.T. of water = 7.0 × 10−2 N/m).
If a drop of liquid breaks into smaller droplets, it results in lowering of temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop in temperature.
The sufrace tension and vapour pressure of water at 20°C is 7.28 × 10–2 Nm–1 and 2.33 × 103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20°C?
Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Find the decrease in the surface area.
We have three identical perfectly black plates. The temperatures of first and third plate is T and 3T. What is the temperature of second plate if system is in equilibrium?
A drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. The ratio of excess pressure inside the drop and bubble is ______.
When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes `(5r)/4`. Taking the atmospheric pressure to be equal to the 10 m height of the water column, the depth of the lake would approximately be ______.
(ignore the surface tension and the effect of temperature)
The excess pressure inside a liquid drop is 500 Nm-2. If the radius of the drop is 2 mm, the surface tension of the liquid is x × 10-3 Nm-1. The value of x is ______.
When one end of the capillary is dipped in water, the height of water column is 'h'. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of capillary is ______.
(Surface tension of water = 7 × 10-2 N/m)
Work done to blow a bubble of volume V is W. The work done in blowing a bubble of volume 2V will be ______.
Calculate (i) the pressure due to the weight of the water at a depth of 2.5 m and (ii) the depth below the surface of water at which the pressure due to the weight of the water equals 1.0 atm.
Define angle of contact.
